{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numba import jit\n",
    "\n",
    "@jit(nopython=True)\n",
    "def deltaE(array, x, y):\n",
    "    deltaE = 2 * array[x, y] * (\n",
    "        array[(x - 2) % (2*L), y] * array[(x - 1) % (2*L), (y - 1) % L] +\n",
    "        array[(x + 2) % (2*L), y] * array[(x + 1) % (2*L), (y - 1) % L] +\n",
    "        array[(x - 1) % (2*L), (y + 1) % L] * array[(x + 1) % (2*L), (y + 1) % L]\n",
    "    )\n",
    "    return deltaE\n",
    "\n",
    "@jit(nopython=True)\n",
    "def w(deltaE, T):\n",
    "    if deltaE <= 0:\n",
    "        return 1.0\n",
    "    else:\n",
    "        return np.exp(-deltaE / T)\n",
    "\n",
    "@jit(nopython=True)\n",
    "def E_array(array):\n",
    "    E = 0\n",
    "    for i in range(2*L):\n",
    "        for j in range(L):\n",
    "            E -= array[i, j] * array[(i - 2) % (2*L), j] * array[(i - 1) % (2*L), (j - 1) % L]\n",
    "    return E\n",
    "\n",
    "@jit(nopython=True)\n",
    "def Metropolis(array, T, steps, reject):\n",
    "    steps += 1\n",
    "    x = np.random.randint(0, 2*L)\n",
    "    y = np.random.randint(0, L)\n",
    "    while array[x, y] == 0:\n",
    "        x = np.random.randint(0, 2*L)\n",
    "        y = np.random.randint(0, L)\n",
    "    delE = deltaE(array, x , y)\n",
    "    if np.random.rand() < w(delE, T):\n",
    "        array[x, y] = -array[x, y]\n",
    "    else:\n",
    "        reject += 1\n",
    "    return steps, reject\n",
    "\n",
    "def sampling(array, T, steps, reject):\n",
    "    E_temp = np.zeros(N2)\n",
    "    M_temp = np.zeros(N2)\n",
    "    for i in range(N2):\n",
    "        for j in range(L * L):\n",
    "            steps, reject = Metropolis(array, T, steps, reject)\n",
    "        E_temp[i] = E_array(array)\n",
    "        M_temp[i] = 2*np.mean(array)\n",
    "    Ising_T.append(array.copy())\n",
    "    E_mean = np.mean(E_temp)\n",
    "    M_mean = np.mean(M_temp)\n",
    "    E.append([T, E_mean/(L*L)])\n",
    "    M.append([T, M_mean])\n",
    "    Cv.append([T, (np.mean(E_temp ** 2) - E_mean ** 2) / (L*L*T * T)])\n",
    "    X.append([T, (np.mean(M_temp ** 2) - M_mean ** 2) / T])\n",
    "    return steps, reject\n",
    "\n",
    "def main():\n",
    "    for T in np.arange(Tmin, Tmax, deltaT):\n",
    "        array = -np.ones((2*L, L), dtype=np.int8)\n",
    "        #array = np.random.choice([-1, 1], size=(2*L, L))\n",
    "        array[1::2, 1::2] = 0\n",
    "        array[::2, ::2] = 0\n",
    "        steps = 0\n",
    "        reject = 0\n",
    "        if T<1:\n",
    "            for i in range(10*N1):\n",
    "                steps,reject = Metropolis(array, T, steps, reject)\n",
    "        else:\n",
    "            for i in range(N1):\n",
    "                steps,reject = Metropolis(array, T, steps, reject)\n",
    "        steps,reject = sampling(array, T, steps, reject)\n",
    "        rejection_rate.append([T, 100*reject / steps])\n",
    "    return\n",
    "\n",
    "L = 40\n",
    "N1 = 500 * L * L\n",
    "N2 = 2000\n",
    "Tmin = 0.1\n",
    "Tmax = 5.0\n",
    "deltaT = 0.05\n",
    "steps = 0\n",
    "reject = 0\n",
    "E = []\n",
    "Ising_T = []\n",
    "M = []\n",
    "Cv = []\n",
    "X = []\n",
    "rejection_rate = []\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "# Define the function\n",
    "def func(T):\n",
    "    return -np.tanh(1 / T)\n",
    "# Generate x values\n",
    "x = np.linspace(0.1, 5, 100)\n",
    "# Generate y values\n",
    "y = func(x)\n",
    "#平均能量\n",
    "plt.scatter([e[0] for e in E], [e[1] for e in E])\n",
    "plt.plot(x, y, color='red',label='Function Curve')\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Average Energy')\n",
    "plt.title('Average Energy vs Temperature')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the function\n",
    "def func(T):\n",
    "    return 1 / (T * np.cosh(1 / T))**2\n",
    "# Generate x values\n",
    "x = np.linspace(0.1, 5, 100)\n",
    "# Generate y values\n",
    "y = func(x)\n",
    "# Plot the heat capacity data\n",
    "plt.scatter([c[0] for c in Cv], [c[1] for c in Cv], label='Heat Capacity')\n",
    "# Plot the function curve\n",
    "plt.plot(x, y, color='red',label='Function Curve')\n",
    "# Add labels and title\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Specific Heat')\n",
    "plt.title('Specific Heat vs Temperature')\n",
    "# Add legend\n",
    "plt.legend()\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#平均磁矩\n",
    "plt.plot([m[0] for m in M], [m[1] for m in M])\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Average Magnetization')\n",
    "plt.title('Average Magnetization vs Temperature')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#磁化率\n",
    "plt.plot([x[0] for x in X], [x[1] for x in X])\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Magnetic Susceptibility')\n",
    "plt.title('Magnetic Susceptibility vs Temperature')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6500000000000001\n"
     ]
    }
   ],
   "source": [
    "maxX = 0\n",
    "Tc = 0.75\n",
    "for x in X:\n",
    "    if x[1] > maxX:\n",
    "        maxX = x[1]\n",
    "        Tc = x[0]\n",
    "print(Tc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#拒绝率\n",
    "plt.plot([r[0] for r in rejection_rate], [r[1] for r in rejection_rate])\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('rejection rate')\n",
    "plt.title('rejection rate vs Temperature')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from scipy.optimize import curve_fit\n",
    "# Tc=0.72\n",
    "# # 温度范围\n",
    "# T = np.arange(Tmin, Tmax, deltaT)\n",
    "# # 比热\n",
    "# Cv_data = np.array([cv[1] for cv in Cv])\n",
    "# # 磁化率\n",
    "# X_data = np.array([x[1] for x in X])\n",
    "# # 磁化强度\n",
    "# M_data = np.array([m[1] for m in M])\n",
    "\n",
    "# # 比热拟合函数\n",
    "# def Cv_fit(T, A, alpha):\n",
    "#     return A * np.abs(T - Tc) ** (-alpha)\n",
    "\n",
    "# # 磁化率拟合函数\n",
    "# def X_fit(T, A, gamma):\n",
    "#     return A * np.abs(T - Tc) ** (-gamma)\n",
    "\n",
    "# # 磁化强度拟合函数\n",
    "# def M_fit(T, A, beta):\n",
    "#     return A * np.abs(Tc - T) ** beta\n",
    "\n",
    "\n",
    "# # 在临界温度附近选取数据点进行拟合\n",
    "# T_fit_left = T[(T <= Tc)&(T >= 0.5)]\n",
    "# Cv_fit_data_left = Cv_data[(T <= Tc)&(T >= 0.5)]\n",
    "# X_fit_data_left = X_data[(T <= Tc)&(T >= 0.5)]\n",
    "# M_fit_data_left = M_data[(T <= Tc)&(T >= 0.5)]\n",
    "\n",
    "# T_fit_right = T[(T >= Tc)&(T <= 3)]\n",
    "# Cv_fit_data_right = Cv_data[(T >= Tc)&(T <= 3)]\n",
    "# X_fit_data_right = X_data[(T >= Tc)&(T <= 3)]\n",
    "\n",
    "# # 比热拟合\n",
    "# popt_Cv_left, _ = curve_fit(Cv_fit, T_fit_left, Cv_fit_data_left)\n",
    "# A_Cv_left, alpha_left = popt_Cv_left\n",
    "\n",
    "# popt_Cv_right, _ = curve_fit(Cv_fit, T_fit_right, Cv_fit_data_right)\n",
    "# A_Cv_right, alpha_right = popt_Cv_right\n",
    "\n",
    "# print(f\"比热临界指数 α (T < Tc) = {alpha_left}\")\n",
    "# print(f\"比热临界指数 α (T > Tc) = {alpha_right}\")\n",
    "\n",
    "# # 磁化率拟合\n",
    "# popt_X_left, _ = curve_fit(X_fit, T_fit_left, X_fit_data_left)\n",
    "# A_X_left, gamma_left = popt_X_left\n",
    "\n",
    "# popt_X_right, _ = curve_fit(X_fit, T_fit_right, X_fit_data_right)\n",
    "# A_X_right, gamma_right = popt_X_right\n",
    "\n",
    "# print(f\"磁化率临界指数 γ (T < Tc) = {gamma_left}\")\n",
    "# print(f\"磁化率临界指数 γ (T > Tc) = {gamma_right}\")\n",
    "\n",
    "# # 磁化强度拟合 (仅对 T < Tc 拟合)\n",
    "# popt_M_left, _ = curve_fit(M_fit, T_fit_left, M_fit_data_left)\n",
    "# A_M_left, beta = popt_M_left\n",
    "\n",
    "# print(f\"磁化强度临界指数 β = {beta}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # 绘图\n",
    "# plt.figure()\n",
    "# plt.plot(T, Cv_data, 'o', label='Cv Data')\n",
    "# plt.plot(T_fit_left, Cv_fit(T_fit_left, *popt_Cv_left), '-', label=f'Fit (T < Tc): α = {alpha_left:.3f}')\n",
    "# plt.plot(T_fit_right, Cv_fit(T_fit_right, *popt_Cv_right), '-', label=f'Fit (T > Tc): α = {alpha_right:.3f}')\n",
    "# plt.xlabel('Temperature')\n",
    "# plt.ylabel('Specific Heat')\n",
    "# plt.legend()\n",
    "# plt.title('Specific Heat vs Temperature')\n",
    "# plt.show()\n",
    "\n",
    "# plt.figure()\n",
    "# plt.plot(T, X_data, 'o', label='X Data')\n",
    "# plt.plot(T_fit_left, X_fit(T_fit_left, *popt_X_left), '-', label=f'Fit (T < Tc): γ = {gamma_left:.3f}')\n",
    "# plt.plot(T_fit_right, X_fit(T_fit_right, *popt_X_right), '-', label=f'Fit (T > Tc): γ = {gamma_right:.3f}')\n",
    "# plt.xlabel('Temperature')\n",
    "# plt.ylabel('Magnetic Susceptibility')\n",
    "# plt.legend()\n",
    "# plt.title('Magnetic Susceptibility vs Temperature')\n",
    "# plt.show()\n",
    "\n",
    "# plt.figure()\n",
    "# plt.plot(T, M_data, 'o', label='M Data')\n",
    "# plt.plot(T_fit_left, M_fit(T_fit_left, *popt_M_left), '-', label=f'Fit: β = {beta:.3f}')\n",
    "# plt.xlabel('Temperature')\n",
    "# plt.ylabel('Average Magnetization')\n",
    "# plt.legend()\n",
    "# plt.title('Average Magnetization vs Temperature')\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# import matplotlib.pyplot as plt\n",
    "# import matplotlib.colors as mcolors\n",
    "\n",
    "\n",
    "# for k in range(len(Ising_T)):\n",
    "#     print(k)\n",
    "#     array = Ising_T[k]\n",
    "#     x = []\n",
    "#     y = []\n",
    "#     colors = []\n",
    "\n",
    "#     # Define offsets for the 6 neighbors in a triangular lattice without horizontal offset\n",
    "#     neighbors_offsets = [\n",
    "#         (-1, -1), (-1, 1), (-2 , 0), \n",
    "#         (2 , 0), (1, -1), (1, 1)\n",
    "#     ]\n",
    "#     # Create a custom color map\n",
    "#     cmap = mcolors.LinearSegmentedColormap.from_list('custom_cmap', ['blue', 'white', 'red'])\n",
    "\n",
    "#     # Normalize the color map based on fixed range [-1, 1]\n",
    "#     norm = mcolors.Normalize(vmin=-1, vmax=1)\n",
    "#     # Collect the points and their colors\n",
    "#     for i in range(2*L):\n",
    "#         for j in range(L):\n",
    "#             if array[i, j] != 0:\n",
    "#                 x.append(i)\n",
    "#                 y.append(j * np.sqrt(3))\n",
    "#                 colors.append(array[i, j])\n",
    "\n",
    "#     plt.figure(figsize=(8, 8))\n",
    "\n",
    "#     # Draw lines between each point and its neighbors\n",
    "#     for i in range(2*L):\n",
    "#         for j in range(L):\n",
    "#             if array[i, j] != 0:\n",
    "#                 x_coord = i\n",
    "#                 y_coord = j * np.sqrt(3) \n",
    "#                 for offset in neighbors_offsets:\n",
    "#                     ni = (i + offset[0])\n",
    "#                     nj = (j + offset[1])\n",
    "#                     if not ni < 0 and not nj < 0 and not ni >= 2*L and not nj >= L:\n",
    "#                         nx_coord = ni\n",
    "#                         ny_coord = nj * np.sqrt(3) \n",
    "#                         if array[i,j]==array[ni,nj]: \n",
    "#                             line_color = cmap(norm(array[i,j]))\n",
    "#                             plt.plot([x_coord, nx_coord], [y_coord, ny_coord], '-', color=line_color, lw=1)\n",
    "\n",
    "#     # Scatter plot for the points\n",
    "#     scatter = plt.scatter(x, y, c=[norm(c) for c in colors], cmap='coolwarm', s=50)\n",
    "#     #plt.colorbar(scatter, label='Spin Value')\n",
    "#     plt.title(f'Temperature = {deltaT*k+Tmin}')\n",
    "#     plt.xlabel('X Position')\n",
    "#     plt.ylabel('Y Position')\n",
    "#     plt.axis('equal')\n",
    "#     plt.show()"
   ]
  }
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